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1.
A closed-form analytical solution of surface motion of a semi-elliptical cylindrical hill for incident plane SH waves is presented. Although some previous analytical work had already dealt with hill topography of semi-circular and shallow circular, our work aims at calculating surface motion of very prolate hill for high incident frequency, and explaining the special vibrating properties of very prolate hill. Accuracy of the solution is checked by boundary conditions, numerical results for surface motion of oblate and prolate hills are calculated, and some conclusions are obtained. 相似文献
2.
Scattering of SH waves by a scalene triangular hill 总被引：1，自引：1，他引：0
<正>The influence of local landforms on ground motion is an important problem.The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function,moving coordinates and auxiliary functions.First,the model is divided into two domains:a scalene triangular hill with a semi-circular bottom;and a half space with a semi-circular canyon.Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains.Then,considering the displacement continuity and stress equilibrium, algebraic equations are established.Finally,numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions. 相似文献
3.
提出了一种新的以层状半空间中周期分布斜线荷载动力格林函数为基本解的间接边界元方法,研究了周期分布凸起地形对平面SH波的散射问题.方法将散射波场分解为凸起内部散射波场和凸起外部散射波场.凸起内部散射波场通过在凸起闭合边界上施加虚拟斜线荷载产生的动力响应来模拟,而凸起外部散射波场则通过在凸起与半空间交界面上施加虚拟周期分布斜线荷载产生的动力响应来模拟.周期分布斜线荷载动力格林函数的引入,使得本文方法仅需针对一个凸起进行边界单元的离散和求解,便可完成问题的求解,避免了通过截断无限边界求解而引入的误差,方法具有较高精度的同时显著降低了求解自由度.文中通过与已有结果的比较,验证了方法的正确性,并以均匀半空间和基岩上单一土层中周期分布凸起为例进行了数值计算分析.研究表明,凸起间距对凸起地形间的动力相互作用有着显著的影响,同时层状半空间中周期分布凸起地形对SH波的散射与均匀半空间情况也有着显著的差别. 相似文献
4.
A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure. 相似文献
5.
Jeng-Tzong Chen Jia-Wei Lee Chine-Feng Wu I-Lin Chen 《Soil Dynamics and Earthquake Engineering》2011,31(5-6):729-736
Following the success of seismic analysis of a canyon [1], the problem of SH-wave diffraction by a semi-circular hill is revisited using the null-field boundary integral equation method (BIEM). To fully utilize the analytical property in the null-field boundary integral equation approach in conjunction with degenerate kernels for solving the semi-circular hill scattering problem, the problem is decomposed into two regions to produce circular boundaries using the technique of taking free body. One is the half-plane problem containing a semi-circular boundary. This semi-infinite problem is imbedded in an infinite plane with an artificial full circular boundary such that degenerate kernel can be fully applied. The other is an interior problem bounded by a circular boundary. The degenerate kernel in the polar coordinates for two subdomains is utilized for the closed-form fundamental solution. The semi-analytical formulation along with matching boundary conditions yields six constraint equations. Instead of finding admissible wave expansion bases, our null-field BIEM approach in conjunction with degenerate kernels have five features over the conventional BIEM/BEM: (1) free from calculating principal values, (2) exponential convergence, (3) elimination of boundary-layer effect, (4) meshless and (5) well-posed system. All the numerical results are comparing well with the available results in the literature. It is interesting to find that a focusing phenomenon is also observed in this study. 相似文献
6.
In this study, the null-field boundary integral equation method (BIEM) and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300. 相似文献
7.
基于黏弹性人工边界的显式动力有限元方法,研究了突出平台状山谷地形场地的地形效应,分析了山谷地形对地表地震动的影响.结果表明:(1)沿着地震动输入方向地表反应较其他方向上的反应强烈;(2)与单一凸起山体地形对地表地震动的放大效应相比,相邻地形的存在对地表地震动位移傅里叶谱谱比曲线的形状影响不大,但是对PGD有着较大的影响... 相似文献
8.
In this paper the boundary element algorithm which uses the time-convoluted traction kernels is applied to a numerical parametric study on the seismic behavior of three-dimensional Gaussian-shaped hills subjected to vertically propagating incident waves. All calculations were executed in the time-domain and the medium was assumed to have a linear elastic constitutive behavior. Results are discussed in both time and frequency domain with respect to the dimensionless parameters. It was shown that wave length and site geometry, including shape and dimension ratios and, to some extent, wave type are the key independent parameters governing hill amplification behavior. Comparing two- and three-dimensional hills with similar shape ratios, two-dimensional hill had greater characteristic periods, where the three-dimensional hill had greater maximum amplification potential. Three-dimensionality has a strong effect on the seismic responses of the hill; however the rate of seismic response variation with the three-dimensionality factor depends on the shape ratio. It was shown that two-dimensional behavior was dominant in low height three-dimensional hills, however, as the shape ratio increased, three-dimensionality effects appeared and the seismic response of the hill tends toward the axisymmetric three-dimensional hill. 相似文献
9.
The ground motion and wave propagation resulting from the scattering of anti-plane (SH) waves by a deep semi-elliptical hill on an elastic half-space are investigated. The solution is the closed-form one based on the method of wave-function expansion, and the expansion of elliptical sine and cosine over the half-range [−π/2, π/2]. The analysis shows that the interference of ground motion depends on several factors such as frequency of the incident waves, incident angle, and the aspect ratio of elliptical hills. Similar to part I: Shallow Hill, numerical results when semi-elliptical tends to semi-circular are compared with the work done by Lee et al. [17]. 相似文献
10.
DIRK GOOSSENS 《地球表面变化过程与地形》1996,21(3):205-216
Wind tunnel experiments of aeolian dust deposition on topographic scale models of ranges of hills were conducted. Different hill sizes and hill spacings were used, and comparisons with the deposition patterns over single, isolated hills were made. Dust profiles over ranges of hills differ from the profiles over identical, but isolated hills. On isolated hills the sedimentation maximum on the windward hillslope is always single and located on the concave part of the slope. In the case of ranges of hills, the maximum is either single or double, with the second peak on the convex part of the windward slope in the latter case. The local sedimentation maximum on the convex leeslope, which is rather unimportant on isolated hills, is much more developed in multiple-hill topography. Also, dust deposition on the leeslopes is significantly higher in multiple-hill topography than on isolated hills. Dust patterns on ranges of hills may be affected by the dust shadow created by the most upstream-located hill. If hills succeed each other quickly, they are located within the shadow zone and are protected from important dust deposition. The plume of high air dust concentration that is created by a hill largely determines the dust pattern on the next hill. As a result of the supply of dust from above by the descending plume, areas that are normally devoid of dust now experience significant dust deposition. 相似文献
11.
This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane. Exact analytical solutions are used for the Green's functions. The boundary integral equation is solved by using numerical techniques. Selected numerical results are presented for the impedances of rectangular and semi-circular rigid strip foundations embedded in four types of anisotropic soils. A discussion on the influence of soil anisotropy and frequency of excitation on the impedances is presented. The versatility of the analysis is demonstrated by considering the through soil interaction between two semi-circular strip foundations. 相似文献
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13.
已有资料显示上蔡岗断裂为隐伏逆断层,为研究上蔡岗断裂浅部构造特征,笔者跨断裂开展高分辨率浅层地震探测,获得4条高分辨率浅层地震剖面。本文根据高分辨率浅层地震剖面,并结合已有地质资料,对上蔡岗断裂浅部特征进行分析和讨论。研究结果表明:上蔡岗断裂为1条走向北北西、倾向北东东的逆断层,在岗地中部存在1条次级断层,与主断层呈反y形构造,与岗地地表形态基本一致。研究结果可为驻马店市地震危险性评价及城市规划提供地质和地球物理学依据。 相似文献
14.
The model studied in this paper presents an extension of previous work for a shear wall on a semi-circular rigid foundation in an isotropic homogeneous and elastic half-space. The objective is to develop a soil-structure interaction model that can later be applied to the case of a flexible foundation. As shown in the Introduction below, Luco considered the case of a rigid foundation subjected to vertical incident plane SH waves, and Trifunac extended the solution for the same rigid foundation subjected to SH waves but for arbitrary angles of the incidence. In this paper, a new approach and model are presented for the same semi-circular rigid foundation with a tapered-shape (instead of rectangular) superstructure. The analytical expression for the deformation of the semi-circular rigid foundation below this tapered shear wall with soil-structure interaction in an isotropic homogeneous and elastic half-space is thus derived. Results are then compared with those of Trifunac discussed in the section below. This problem formulation can and will later be extended in the case of a flexible foundation that is semi-circular or arbitrarily shaped. 相似文献
15.
本文推广了经典的抽样定理,并据此导出了函数有限离散傅里叶变换误差方程（简称DFT误差方程,下同）。该方程把有限离散傅里叶变换中固有的离散效应和有限效应表示为确切的数学形式。离散效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数;有限效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数的DFT。 基于DFT误差方程和位函数特点,作者提出了两种位场数值傅里叶变换新算法--移样法和等效源续尾叠样法。移样法可近百倍地提高位场数值傅里叶反变换的精度,等效源续尾叠样法可数十倍地提高正变换精度。两种算法都不需要增加资料长度和取样密度,因而基本不需要增加计算机时间和内存。文中给出了算例。 相似文献
16.
SH波入射时半圆形凸起与凹陷地形的地震动 总被引：2，自引：0，他引：2
研究了弹性半空间中半圆形凸起与凹陷相连地形对SH波的散射问题。将整个求解区域分割为2部分,在其中分别构造满足边界条件的位移解,通过移动坐标使之满足“公共边界”以及半圆形凹陷表面上的边界条件,从而建立起求解该问题的无穷代数方程组。最后,给出了地表位移幅值的数值结果以及凸起地形顶点和凹陷地形最低点处位移幅值的反应谱并进行了讨论。 相似文献
17.
Application of the weighted residual method to diffraction by 2-D canyons of arbitrary shape: I. Incident SH waves 总被引：1，自引：0，他引：1
A solution for the two-dimensional scattering and diffraction of plane SH waves by canyons of arbitrary shape in an elastic half space is presented. The wave field for arbitrary geometry in this paper is computed numerically by the method of weighted residues (moment method). The wave displacement field computed by the present residual method for the case of a semi-circular canyon was shown to agree analytically and numerically with that computed by the exact closed form series solution. The same observations about ground amplifications, their dependence on frequencies and orientations of the incident waves, can be stated here for canyons of arbitrary shape as previously made for circular canyons. 相似文献
18.
利用我们建立的三维分层线性理论计算模式和中尺度数值模式ARPS, 分别研究了三维分层流动过双山脉地形产生的三维线性和非线性山脉重力波和大气船舶的结构特征及其形成机制.线性理论计算结果表明三维三层流动过双山脉地形时，两个山脉各自强迫出一个发散模态的山脉背风波，在第二个山脉背风面，三维三层流动过双山脉地形可以强迫出两个发散模态的拦截背风波，大大加强了对大气环流的拖曳作用.非线性数值模拟结果表明，流动过山所产生的非线性山脉重力波和大气船舶完全不同于三维分层线性理论计算模式所产生的山脉重力波和大气船舶的结构和特征，由于分层流体之间的非线性相互作用，三维三层流动过双山脉地形时，可在第二个山脉背风面激发4个发散模态的拦截背风波. 三维三层流动过双山脉地形所强迫的山脉重力波和大气船舶，具有同三维三层流动过孤立山脉所产生的山脉重力波和大气船舶完全不同的结构和特征，三维流动过双山脉地形对两个山脉之间的距离表现出极大的敏感性.对于相距较远的两个山脉，流动过双山脉所强迫的山脉重力波表现为4个发散模态的拦截背风波，波动的能量相对于相距较近的两个山脉能传播到更高的高度. 相似文献
19.
Tien-Chang Lee 《Pure and Applied Geophysics》1991,135(1):1-13
The theory of heat-flow variation over a Lees-type hill is well known for evaluating terrain effects on terrestrial heat flow. However, a hill cannot be converted into a valley by simply changing the sign of one of the terrain-defining parameters, nor can several Lees' hills be superposed to simulate a series of hills and valleys for correcting a terrain-induced disturbance of heat flow. The proper derivations for a Lees-type valley are presented and the superposition is compared with analytic solutions for two parallel semi-cylindrical valleys and two semi-spherical basins embedded in an otherwise planar ground. Generally, heat flux climaxes over central valleys or basins, and dips toward their margins where rapid change in topography occurs. Variation of heat flux induced by a three-dimensional terrain is relatively large, as compared to two-dimensional features, but its areal extent is relatively limited. The two-dimensional effects also extend relatively deeper. In applying two-dimensional algorithms to a three-dimensional terrain, the correction may be over- or underestimated depending on the distance from a borehole to prominent terrain features in the surrounding area. 相似文献
20.
利用波函数的Fourier-Bessel级数展开法,推导出了含任意多个圆弧状沉积层的谷地在Rayleigh波入射下二维稳态动力响应的解析解,分析了该级数形式解析解随截断项数的收敛问题,讨论了在获取该解析解的过程中,用于计算Rayleigh波自由场的有限Fourier级数的项数和用于模拟水平地表的大圆弧的半径对解的影响.研究结果表明,该解析解能够在一个非常宽的频带内收敛.最后,利用该解析解,在一个较宽的频带范围内,讨论了谷地中沉积介质的成层性,包括沉积层的层数、软弱夹层的存在及其厚度等因素对地面运动的影响. 相似文献